You can identify prime numbers visually by arranging dots into columns and rows. Numbers that can be arranged into neat rows and columns are NOT prime numbers (i.e., composite numbers). By neat, I mean that there are no incomplete rows and columns.
Greatest Common Factor (GCF) is the largest number that is a factor of other numbers. For example, the GCF of 14 and 35 is 7. Seven is the largest grouping (factor) that can be made from both numbers.
How many factors?
You can determine the number of factors of a number by using the exponents of its prime factor tree.
Add one to the exponent for each prime factor and multiply them.
there are 4 two's, so adding one to the exponent makes it 5.
There is 1 three, so adding one to the exponent makes it 2.
5 x 2 = 10 (there are 10 factors of 48)
Visualizing Least Common Multiple
Least Common Multiple (LCM) is the smallest number is a multiple of other numbers. For example, let's say you have three different sized blocks of 3, 5, and 6 units. The LCM is 30. That is the smallest number that has the factors 3, 5, and 6.
GCF & LCM of several numbers
Finding the GCF is the same process no matter how many numbers are involved. Simply find the prime factors that are common to ALL numbers. Finding the LCM of more than two numbers is more complicated than finding the LCM of two numbers. See the example below. Notice how you identify the prime factors common to three numbers, then two numbers.
An Explation of Greatest Common Factor (GCF) & Least Common Multiple (LCM)
Prime factorization of numbers between 1 and 197
For a list of numbers and their prime factors beyond 197, click here
Link to a webpage that computs the prime fators of a number
If you want more of a graphical representation of the prime factor tree (see example below), you can download an app that creates prime factor trees (FactorTrees.nbp).
You must also download and install the this player (link)
Numeric Factors (Unit 2)
This math unit centers around the concept of prime numbers, which are the building blocks of all other numbers.
Unit 2 Schedule
no class
50 minutes
60 minutes
no class
45 minutes
70 minutes
40 minutes
70 minutes
90 minutes
70 minutes
no class
Additional Problems for this Unit
Visualizing Prime Numbers
You can identify prime numbers visually by arranging dots into columns and rows. Numbers that can be arranged into neat rows and columns are NOT prime numbers (i.e., composite numbers). By neat, I mean that there are no incomplete rows and columns.
Composite Number
Prime Number
Visualizing Greatest Common Factor
Greatest Common Factor (GCF) is the largest number that is a factor of other numbers. For example, the GCF of 14 and 35 is 7. Seven is the largest grouping (factor) that can be made from both numbers.
How many factors?
You can determine the number of factors of a number by using the exponents of its prime factor tree.
Add one to the exponent for each prime factor and multiply them.
there are 4 two's, so adding one to the exponent makes it 5.
There is 1 three, so adding one to the exponent makes it 2.
5 x 2 = 10 (there are 10 factors of 48)
Visualizing Least Common Multiple
Least Common Multiple (LCM) is the smallest number is a multiple of other numbers. For example, let's say you have three different sized blocks of 3, 5, and 6 units. The LCM is 30. That is the smallest number that has the factors 3, 5, and 6.
GCF & LCM of several numbers
Finding the GCF is the same process no matter how many numbers are involved. Simply find the prime factors that are common to ALL numbers. Finding the LCM of more than two numbers is more complicated than finding the LCM of two numbers. See the example below. Notice how you identify the prime factors common to three numbers, then two numbers.
An Explation of Greatest Common Factor (GCF) & Least Common Multiple (LCM)
Prime factorization of numbers between 1 and 197
For a list of numbers and their prime factors beyond 197, click here
Resources
Least Common Denominator
eTextbook page 100
Finding common denominators (Khan Academy video)
Adding fractions with unlike denominators (Khan Academy video)
Simplifying Fractions
students contribution
Simplifying Square Roots
Understanding Square Roots (Khan Academy video)
Rules of Divisibility
students contribution
Prime Factor trees
Link to a webpage that computs the prime fators of a number
If you want more of a graphical representation of the prime factor tree (see example below), you can download an app that creates prime factor trees (FactorTrees.nbp).
You must also download and install the this player (link)
extra credit
simplifying radicals (Khan Academy video)
more simplifying radicals (Khan Academy video)